Scaling Laws of Multicast Capacity for Power-Constrained Wireless Networks under Gaussian Channel Model

We study the asymptotic networking-theoretic multicast capacity bounds for random extended networks (REN) under Gaussian channel model, in which all wireless nodes are individually power-constrained. During the transmission, the power decays along path with attenuation exponent α >; 2. In REN, n nodes are randomly distributed in the square region of side length √n. There are n<sub>s</sub> randomly and independently chosen multicast sessions. Each multicast session has n<sub>d</sub> + 1 randomly chosen terminals, including one source and n<sub>d</sub> destinations. By effectively combining two types of routing and scheduling strategies, we analyze the asymptotic achievable throughput for all n<sub>s</sub> = ω(1) and nd. As a special case of our results, we show that for n<sub>s</sub> = Θ(n), the per-session multicast capacity for REN is of order Θ(1/√n<sub>d</sub>n) when nd = O(n/(log n)<sup>a+1</sup>) and is of order Θ(1/n<sub>d</sub> · (log n)<sup>-n/2</sup>) when n<sub>d</sub> = Ω(n/log n).

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